= Nonvanishing of holomorphic differentials in genus one
{title2=$\eta\ne0\Longrightarrow(\eta)=0$}
Every nonzero <holomorphic differential form> on a <compact Riemann surface> of <genus> one is nowhere zero. Its <canonical divisor> is an <effective divisor> of degree $2g-2=0$, and hence has every coefficient zero. In particular, such a differential trivializes the <canonical bundle>. This assertion concerns the differential itself, not the individual factors in a representation $f\,dh$.
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